# Documentation

## Module urban_sarca_lib

Urban Green SARCA library includes functions usable for quick estimation of radioactive deposition of the surface.

`urban_sarca_lib.``contBiomass`(depo, IF)

  Radiaoctive contamination of biomass

  Parameters: | depo – Total radioactive deposition IF – Interception Factor (rel.)
  Returns: | Radioactive contamination of biomass

`urban_sarca_lib.``contMass`(cont_biomass, fresh_biomass)

  Calculation radioactive contamination of fresh vegetation mass

  Parameters: | cont_biomass – Radioactive deposition on biomass fresh_biomass – Amount of fresh biomass of vegetation
  Returns: | Fresh vegetation mass radioactive contamination

`urban_sarca_lib.``contSoil`(depo, IF)

  Radiaoctive contamination of soil

  Parameters: | depo – Total radioactive deposition IF – Interception Factor (rel.)
  Returns: | Radioactive contamination of soil

`urban_sarca_lib.``hygLimit`(cont_mass, hyg_lim=1000)

  Mask for hygienic limit of biomass radioactive contamination exceeding.

  Parameters: | cont_mass – Fresh vegetation mass radioactive contamination hyg_lim – Hygienic limit of mass radioactive contamination . Default value is 1000 according to Czech law.
  Returns: | Mask for hygienic limit of biomass radioactive contamination exceeding.

`urban_sarca_lib.``interceptFactor`(LAI, precip, fresh_biomass, k=1.0, S=0.2)

  Interception factor for both dry and wet deposition of radionuclides.

  Parameters: | LAI – Leaf Area Index (unitless) k – Constant of radionuclide: I = 0.5, Sr and Ba = 2.0, Cs and another radionuclides = 1.0 precip – Precipitation amount (mm) for period of deposition (ca 24 hours after radiation accident). fresh_biomass – Amount of fresh biomass S – Mean thickness of water film at plant leaves (mm). Default S = 0.2 mm
  Returns: | Interception Factor (rel.)

`urban_sarca_lib.``referLevel`(depo, ref_level1=5000, ref_level2=3000000)

  Mask of radioactive deposition for three reference levels (categories):

  0: Low

  1: Middle

  2: High

  Parameters: | depo – Total radioactive deposition ref_level1 – Lower reference level treshold . Default value = 5000 ref_level2 – Upper reference level treshold . Default value = 3000000
  Returns: | Mask of radioactive deposition for three reference levels

## Module SEBCS_lib

Module SEBCS_lib is library of SEBCS software (Brom 2020) designed for geographical and remotely sensed purposes, mainly for analysis of energy balance of the surface. Some methods are used within Urban Green SARCA software.

class `SEBCS_lib.``GeoIO`

  Class includes functions for reading of geotransformation features from raster and for writing ne rasters from numpy arrays.

  `arrayToRast`(arrays, names, prj, gtransf, EPSG, out_folder, driver_name='GTiff', out_file_name=None, multiband=False)

    Export numpy 2D arrays to multiband or singleband raster files. Following common raster formats are accepted for export:

    - ENVI .hdr labeled raster format
    - Erdas Imagine (.img) raster format
    - Idrisi raster format (.rst)
    - TIFF / BigTIFF / GeoTIFF (.tif) raster format
    - PCI Geomatics Database File (.pix) raster format

    Parameters: | arrays (numpy.ndarray, list) – Numpy array or list of arrays for export to raster. names (str, list) – Name or list of names of the exported bands (in case of multiband raster) or particular rasters (in case of singleband rasters). prj (str) – Projection information of the exported raster (dataset). gtransf (tuple) – The affine transformation coefficients. EPSG (int) – EPSG Geodetic Parameter Set code. out_folder (str) – Path to folder where the raster(s) will be created. driver_name (str) – GDAL driver. ‘GTiff’ is default. out_file_name (str) – Name of exported multiband raster. multiband (bool) – Option of multiband raster creation.
    Returns: | Raster singleband or multiband file(s)
    Return type: | raster

  `lyrsExtent`(in_lyrs_list)

    Check differences between size of the input layers. Function compares rasters only on basis of number of columns and rows.

    Parameters: | in_lyrs_list (list) – List of layers (Numpy 2D arrays).
    Returns: | True

  static `rasterToArray`(layer)

    Conversion of raster layer to numpy array.

    Parameters: | layer (str) – Path to raster layer.
    Returns: | raster file converted to numpy array
    Return type: | numpy.ndarray

  `readGeo`(rast)

    Reading geographical information from raster using GDAL.

    Parameters: | rast (str) – Path to raster file in GDAL accepted format.
    Returns: | The affine transformation coefficients.
    Return type: | tuple
    Returns: | Projection information of the raster (dataset).
    Return type: | str
    Returns: | Pixel width (m) on X axis.
    Return type: | float
    Returns: | Pixel height (m) on Y axis.
    Return type: | float
    Returns: | EPSG Geodetic Parameter Set code.
    Return type: | int

class `SEBCS_lib.``HeatFluxes`

  Calculation of heat fluxes and heat balance features from spectral and thermal spatial data and meteorological measurements. The class contains a set of methods for calculation heat balance, e.g. ground heat flux, sensible heat flux, latent heat flux, evaporative fraction, omega factor (decoupling coefficient), surface resistance for water vapour transfer etc. Calculation for both aerodynamic and gradient method is included.

  `aeroEF`(LE, Rn, G)

    Evaporative fraction calculated using aerodynamic method (rel.).

    Parameters: | LE (numpy.ndarray) – Latent heat flux Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux
    Returns: | Evaporative fraction (rel.)
    Return type: | numpy.ndarray

  `bowen`(flux_H, LE)

    Bowen ratio according to Bowen (1926)

    Parameters: | flux_H (numpy.ndarray) – Sensible heat flux LE (numpy.ndarray) – Latent heat flux
    Returns: | Bowen ratio (unitless)
    Return type: | numpy.ndarray

  `cwsi`(LEp, ra, rc, E_Z_sat, e_Z, rho, delta, gamma, cp=1012)

    Crop Water Stress Index calculated according to Jackson et al. ( 1981, 1988).

    Parameters: | LEp (numpy.ndarray) – Potential evaporation latent heat flux ra (numpy.ndarray) – Aerodynamic resistance rc – Surface resistance for water vapour transfer E_Z_sat (numpy.ndarray) – Saturated water vapour pressure (kPa). e_Z (numpy.ndarray) – Water vapour pressure (kPa). rho (numpy.ndarray) – Specific air density delta (numpy.ndarray) – Delta function gamma (numpy.ndarray) – Psychrometric constant . cp (float) – Thermal heat capacity of dry air
    Returns: | Crop Water Stress Index (CWSI)
    Return type: | numpy.ndarray

  `fluxHAer`(ra, rho, dT, cp=1012.0)

    Sensible heat flux calculated using aerodynamic method.

    Parameters: | ra (numpy.ndarray) – Aerodynamic resistance for heat and momentum transfer calculated according to Thom (1975) rho (numpy.ndarray) – Specific air density dT (numpy.ndarray) – Temperature gradient calculated according to SEBAL (Bastiaanssen et al. 1998) cp (float) – Thermal heat capacity of dry air
    Returns: | Sensible heat flux
    Return type: | numpy.ndarray

  `fluxLE`(Rn, G, flux_H)

    Latent heat flux

    Parameters: | Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux flux_H (numpy.ndarray) – Sensible heat flux
    Returns: | Latent heat flux
    Return type: | numpy.ndarray

  `fluxLE_EQ`(Rn, G, delta, gamma)

    Equilibrium evaporation rate .

    Parameters: | Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux delta (numpy.ndarray) – Delta function gamma (numpy.ndarray) – Psychrometric constant .
    Returns: | Equilibrium evaporation latent heat flux .
    Return type: | numpy.ndarray

  `fluxLE_PT`(LE_eq, alpha=1.26)

    Evaporation from wet surface according to Priestley-Taylor (1972).

    Parameters: | LE_eq (numpy.ndarray) – Equilibrium evaporation latent heat flux alpha (float) – Priestley-Taylor alpha.
    Returns: | Latent heat flux for wet surface calculated by Priestley-Taylor
    Return type: | numpy.ndarray

  `fluxLE_p`(Rn, G, delta, VPD, ra, gamma, rho, cp=1012.0)

    Latent heat flux for potential evapotranspiration according to Penman (1948) .

    Parameters: | Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux delta (numpy.ndarray) – Delta function VPD (numpy.ndarray) – Water vapour pressure in air (kPa) ra (numpy.ndarray) – Aerodynamic resistance gamma (numpy.ndarray) – Psychrometric constant . rho (numpy.ndarray) – Specific air density cp (float) – Thermal heat capacity of dry air
    Returns: | Potential evaporation latent heat flux .
    Return type: | numpy.ndarray

  `fluxLE_ref`(Rn, G, ta, ts, U, Rh, DMT, veg_type='short', cp=1012.0)

    Latent heat flux for reference evapotranspiration according to FAO56 method (Allen et al. 1998, ASCE-ET 2000)

    Parameters: | Rn (numpy.ndarray, float) – Rn: Total net radiation G (numpy.ndarray, float) – Ground heat flux ta – Air temperature measured at meteostation at approx. 2 m.

    :type ta: numpy.ndarray, float :param ts: Surface temperature measured at meteostation at approx. 2 m. :param U: Wind speed measured at meteostation :type U: numpy.ndarray, float :param Rh: Relative humidity (%) :type Rh: numpy.ndarray, float :param DMT: Digital model of terrain or altitude (m a.s.l.) :type DMT: numpy.ndarray, float :param veg_type: Type of vegetation - “short” or “tall” :type veg_type: str :param cp: Thermal heat capacity of dry air :type cp: float

    Returns: | Latent heat flux for reference evapotranspiration.
    Return type: | numpy.ndarray, float

    References

    Allen, R. et al., 1998. Crop Evapotranspiration: Guidelines for Computing Crop Water Requirements. United Nations Food and Agriculture Organization, Irrigation and Drainage Paper 56, Rome, Italy. 300 pp. *ASCE-ET 2000: ASCE’s Standardized Reference Evapotranspiration Equation. National Irrigation Symposium in Phoenix, Arizona, US.

  `gamma_x`(rcp, ra, gamma)

    Psychrometric constant corrected on the rcp and ra according to Jackson et al. (1981, 1988).

    Parameters: | rcp (numpy.ndarray) – Surface resistance for water vapour transfer for potential evapotranspiration . ra (numpy.ndarray) – Aerodynamic resistance gamma (numpy.ndarray) – Psychrometric constant .
    Returns: | Psychrometric constant corrected on the rcp and ra according to Jackson et al. (1981, 1988) ..
    Return type: | numpy.ndarray

  `gradEF`(ts, ta, mask=None)

    Evaporative fraction calculated from gradient method according to Suleiman and Crago (2004).

    Parameters: | ts (numpy.ndarray) – Surface temperature ta (numpy.ndarray, float) – Air temperature mask – Mask of the area of interest. Number of rows and columns

    should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray

    Returns: | Evaporative fraction (rel.)
    Return type: | numpy.ndarray

  `gradH`(LE, Rn, G)

    Sensible heat flux calculated using gradient method.

    Parameters: | LE (numpy.ndarray) – Latent heat flux Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux
    Returns: | Sensible heat flux
    Return type: | numpy.ndarray

  `gradLE`(EF, Rn, G)

    Latent heat flux calculated using gradient method .

    Parameters: | EF – Evaporative fraction (rel.) Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux
    Returns: | Latent heat flux
    Return type: | numpy.ndarray

  `groundFlux`(ndvi, Rn, ts, albedo)

    Ground heat flux according to Bastiaanssen et al. (1998)

    Parameters: | ndvi (numpy.ndarray) – NDVI spectral vegetation index (unitless) Rn (numpy.ndarray) – Total net radiation ts (numpy.ndarray) – Surface temperature albedo (numpy.ndarray) – Albedo (rel.)
    Returns: | Ground heat flux
    Return type: | numpy.ndarray

  `heatFluxes`(Rn, G, ts, ta, method='aero', Uz=None, h_eff=None, LAI=None, z0m=None, z0h=None, rho=None, disp=None, mask=None, air_pressure=101.3, Z=200.0, cp=1012, L=-10000.0, n_iter=10, a=1.0, b=0.667, c=5.0, d=0.35, kappa=0.41, gravit=9.81)

    Function provides a calculation for heat fluxes, aerodynimc resistance of surface and friction velocity for three different methods: 1. “aero” - Aerodynamic method based on Monin-Obukhov theory 2. “sebal” - Method based on SEBAL approach provided by

    > Bastiaanssen et al.

    > > param disp: |
    > > param Rn: | Total net radiation
    > > type Rn: | numpy.ndarray
    > > param G: | Ground heat flux
    > > type G: | numpy.ndarray
    > > param ts: | Surface temperature
    > > type ts: | numpy.ndarray
    > > param ta: | Air temperature
    > > type ta: | numpy.ndarray, float
    > > param method: | Method of heat fluxes calculation: aero - Aerodynamic method based on calculation of ra using approach proposed by Thom (1975) SEBAL - SEBAL method proposed by Bastiaanssen et al. (1998) grad - Gradient method proposed by Suleiman and Crago (2004)
    > > type method: | str
    > > param Uz: | Wind speed measured on meteostation at level Z_st .
    > > type Uz: | float, numpy.ndarray
    > > param h_eff: | Effective height of vegetation cover
    > > type h_eff: | numpy.ndarray, float
    > > param LAI: | Leaf area index
    > > param z0m: | Aerodynamic roughness of the surface for momentum

    > > transfer (m) :type z0m: numpy.ndarray :param z0h: Aerodynamic roughness of the surface for heat transfer (m) :type z0h: numpy.ndarray :param rho: Volumetric dry air density :type rho: numpy.ndarray, float :param disp: Zero plane displacement (m) :type disp: numpy.ndarray, float :param mask: Mask of the area of interest. Number of rows and columns should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray :param air_pressure: Air pressure at level Z (kPa) :type air_pressure: float, numpy.ndarray :param Z: Blending height (m) :type Z: float :param cp: Thermal heat capacity of dry air :type cp: float :param L: Initial Monin-Obukhov lenght (m). :type L: float :param n_iter: Number of iteration in stability coefficient calculation. :type n_iter: int :param a: Constant for stability parameters calculation (Beljaars and Holtslag, 1991) :type a: float :param b: Constant for stability parameters calculation (Beljaars and Holtslag, 1991) :type b: float :param c: Constant for stability parameters calculation (Beljaars and Holtslag, 1991) :type c: float :param d: Constant for stability parameters calculation (Beljaars and Holtslag, 1991) :type d: float :param kappa: von Karman constant. Default 0.41 :type kappa: float :param gravit: Gravitation forcing (m/s2). Default 9.81 :type gravit: float

    > > returns: | Sensible heat flux
    > > rtype: | numpy.ndarray
    > > returns: | Latent heat flux
    > > rtype: | numpy.ndarray
    > > returns: | Evaporative fraction (rel.)
    > > rtype: | numpy.ndarray
    > > returns: | Latent heat flux for equilibrium evaporation :math:`(W.m^{

    > > -2})` :rtype: numpy.ndarray :returns: Latent heat flux for Priestley-Taylor evaporation :rtype: numpy.ndarray :returns: Aerodynamic resistance for heat and momentum transfer :rtype: numpy.ndarray :returns: Friction velocity

    > > References

    > > Bastiaanssen, W.G.M., Menenti, M., Feddes, R.A., Holtslag, A.A.M., 1998. A remote sensing surface energy balance algorithm for land ( SEBAL). 1. Formulation. Journal of Hydrology 212–213, 198–212. https://doi.org/10.1016/S0022-1694(98)00253-4

    > > Beljaars, A.C.M., Holtslag, A.A.M., 1991. Flux Parametrization over Land Surfaces for Atmospheric Models. Journal of Applied Meteorology 30, 327–341. https://doi.org/10.1175/1520-0450( 1991)030<0327:FPOLSF>2.0.CO;2

    > > Suleiman, A., Crago, R., 2004. Hourly and Daytime Evapotranspiration from Grassland Using Radiometric Surface Temperatures. Agronomy Journal 96, 384–390. https://doi.org/10.2134/agronj2004.3840

    > > Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.

  `intensityE`(LE, latent)

    Evaporation intensity in .

    Parameters: | LE (numpy.ndarray) – Latent heat flux latent (numpy.ndarray) – Latent heat of water evaporation .
    Returns: | Intensity of water evaporation .
    Return type: | numpy.ndarray

  `omega`(LE, LE_p)

    Omega factor (Decoupling coefficient) according to Jarvis and McNaughton (1985)

    Parameters: | LE (numpy.ndarray) – Latent heat flux LE_p (numpy.ndarray) – Potential evaporation latent heat flux
    Returns: | Omega factor (unitless)
    Return type: | numpy.ndarray

    References:

    Jarvis, P., McNaughton, K., 1986. Stomatal Control of Transpiration: Scaling Up from Leaf to Region, in: Advances in Ecological Research. Elsevier, pp. 1–49.

  `rcp`(E_Z_sat, e_Z, rho, LE_p, ra, gamma, cp=1012.0)

    Surface resistance for water vapour transfer for potential evapotranspiration .

    Parameters: | E_Z_sat (numpy.ndarray) – Saturated water vapour pressure (kPa). e_Z (numpy.ndarray) – Water vapour pressure (kPa). rho (numpy.ndarray) – Specific air density LE_p (numpy.ndarray) – Potential evaporation latent heat flux ra (numpy.ndarray) – Aerodynamic resistance gamma (numpy.ndarray) – Psychrometric constant . cp (float) – Thermal heat capacity of dry air
    Returns: | Surface resistance for water vapour transfer for potential evapotranspiration .
    Return type: | numpy.ndarray

  `rs`(delta, gamma, omega, ra)

    Surface resistance for water vapour transfer

    Parameters: | delta (numpy.ndarray) – Delta function gamma (numpy.ndarray) – Psychrometric constant . omega (numpy.ndarray) – Decoupling coefficient (rel.) ra (numpy.ndarray) – Aerodynamic resistance
    Returns: | Surface resistance for water vapour transfer
    Return type: | numpy.ndarray

class `SEBCS_lib.``MeteoFeatures`

  Calculation of basic meteorological features and miscellaneous variables.

  `airDensity`(ta)

    Volumetric dry air density .

    Parameters: | ta (numpy.ndarray, float) – Air temperature
    Returns: | Volumetric dry air density
    Return type: | numpy.ndarray, float

  `airPress`(ta, DMT, Z=200.0, P0=101.325, adiabatic=0.0065)

    Atmospheric air pressure at level Z (kPa)

    Parameters: | ta (numpy.ndarray, float) – Air temperature DMT (numpy.ndarray, float) – Digital elevation model or altitude (m) Z (float) – Height of measurement above surface (m) P0 (float) – Sea level air pressure (kPa) adiabatic (float) – Adiabatic lapse rate
    Returns: | Air pressure at level Z (kPa)
    Return type: | numpy.ndarray, float

  `airTemp`(ta_st, st_altitude, DMT, adiabatic=0.0065)

    Conversion of air temperature calculated from temperature data and digital elevation model to spatial near to ground temperature or temperature at different altitude.

    Parameters: | ta_st – Air temperature measured on meteostation :math:`(SI{

    }degreeCelsius)` :type ta_st: float :param st_altitude: Meteostation altitude (m a.s.l.) :type st_altitude: float :param DMT: Digital elevation model (m) or altitude for calculation of ta value. :type DMT: numpy.ndarray, float :param adiabatic: Adiabatic lapse rate . Default = 0.0065 :type adiabatic: float :return: Spatial air temperature :rtype: numpy.ndarray, float

  `airTemperatureBlending`(ta_surface, Z=200.0, Z_st=2.0, adiabatic=0.0065)

    Conversion of spatial air temperature measured for near surface level to level Z above the surface. This approach is usually used for calculation of air temperature at blending height (mixing layer).

    Parameters: | ta_surface – Spatial air temperature for near ground level (

    Z_st; :type ta_surface: :param Z: Height of a level which is used for calculation. Default value corresponds with “blending” height or height of mixing layer. Default is 200 m above surface. :type Z: float :param Z_st: Height of air temperature measurement (m) :type Z_st: float :param adiabatic: Adiabatic lapse rate . Default = 0.0065 :type adiabatic: float :return:

  `delta`(ts, ta)

    Slope of water vapour pressure gradient to temperature gradient - delta function . Calculation according to Jackson et al. (1998).

    Parameters: | ts (numpy.ndarray) – Surface temperature ta (numpy.ndarray, float) – Air temperature
    Returns: | Slope of water vapour pressure gradient to temperature gradient - delta function
    Return type: | numpy.ndarray

  `emissivity`(red, ndvi)

    Surface emissivity calculated according to Sobrino et al. (2004) NDVI Treshold Method.

    Parameters: | red (numpy.ndarray) – Spectral reflectance in RED region (rel.) ndvi (numpy.ndarray) – Spectral vegetation index NDVI (unitless)
    Returns: | Surface emissivity (rel.)
    Return type: | numpy.ndarray

  `gamma`(airP, latent, cp=1012.0)

    Psychrometric constant .

    Parameters: | airP (numpy.ndarray, float) – Atmospheric pressure (kPa) latent – Latent heat for water vapour exchange cp (float) – Thermal heat capacity of dry air
    Returns: | Psychrometric constant
    Return type: | numpy.ndarray, float

  `latent`(ta)

    Latent heat for the water vapour exchange .

    Parameters: | ta (numpy.ndarray, float) – Air temperature
    Returns: | Latent heat for the water vapour exchange
    Return type: | numpy.ndarray, float

  `satVapourPress`(ta)

    Saturated water vapour pressure (kPa) calculated using Magnus-Tetens equation.

    Parameters: | ta (numpy.ndarray, float) – Air temperature
    Returns: | Saturated water vapour pressure (kPa)
    Return type: | numpy.ndarray, float

  `surfaceTemperature`(tir_band, emissivity=1.0, emis_rule='No')

    Correction of surface temperature on emissivity. :param tir_band: Layer of surface temperature

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    . :type tir_band: numpy.ndarray :param emissivity: Layer of emissivity (rel.). :type emissivity: numpy.ndarray :param emis_rule: Setting if the correction will be done or not.

    > No is default.

    Returns: | Layer of corrected surface temperature :math:`(SI{

    }degreeCelsius)`. :rtype: numpy.ndarray

  `vapourPress`(E_sat, Rh)

    Water vapour pressure in air (kPa).

    Parameters: | E_sat (numpy.ndarray, float) – Saturated water vapour pressure (kPa) Rh (numpy.ndarray, float) – Relative humidity of air (%)
    Returns: | Water vapour pressure in air (kPa)
    Return type: | numpy.ndarray, float

  `vpd`(E_sat, e_abs)

    Water vapour pressure deficit (kPa).

    Parameters: | E_sat (numpy.array, float) – Saturated water vapour pressure (kPa) e_abs (numpy.array, float) – Water vapour pressure in air (kPa)
    Returns: | Water vapour pressure deficit (kPa)
    Return type: | numpy.ndarray, float

class `SEBCS_lib.``SolarRadBalance`

  Class contains functions for calculation of solar radiation balance and topographic features: incident radiation in dependence on surface geometry, slope of terrain, aspect of terrain, albedo, longwave radiation fluxes and atmospheric emissivity, shortwave radiation reflectance and total net radiation

  `albedo`(band_red, band_nir, sat_type='L8', band_blue=None, band_green=None, band_sw1=None, band_sw2=None)

    Calculation of Albedo according to data type (satellite data type) or data availability. Albedo can be calculated using Landsat data or using any data including RED and NIR band. For the Landsat 8 data Olmedo method is used, for tle Landsat 4, 5 and 7 Tasumi approach is used. If only RED and NIR bands are available, Brom method is used.

    Parameters: | band_red (numpy.ndarray) – Red band (rel.) band_nir (numpy.ndarray) – NIR band (rel.) sat_type (str) – Type of Landsat satellite: L5 - Landsat 4 TM, 5 TM or Landsat 7 ETM+ L8 - Landsat 8 OLI/TIRS band_blue (numpy.ndarray) – Blue band (rel.) band_green (numpy.ndarray) – Green band (rel.) band_sw1 (numpy.ndarray) – SWIR1 band on ca 1.61 (rel.) band_sw2 (numpy.ndarray) – SWIR2 band on ca 2.2 (rel.)
    Returns: | Albedo (rel.)
    Return type: | numpy.ndarray

    References:

    G.F. Olmedo, S. Ortega-Farias, D. Fonseca-Luengo, D. de la Fuente-Saiz, F.F. Peñailillo 2018: Water: actual evapotranspiration with energy balance models. R Package Version 0.6 (2017)

    Tasumi, M., Allen, R.G., Trezza, R., 2008. At-Surface Reflectance and Albedo from Satellite for Operational Calculation of Land Surface Energy Balance. Journal of Hydrologic Engineering 13, 51–63. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:2(51).

    Duffková, R., Brom, J., Žížala, D., Zemek, F., Procházka, J., Nováková, E., Zajíček, A., Kvítek, T., 2012. Určení infiltračních oblastí pomocí vodního stresu vegetace na základě dálkového průzkumu Země a pozemních měření. Certifikovaná metodika. VÚMOP, v.v.i., Praha.

  `albedoBrom`(ndvi, msavi, c_a=0.08611, c_b=0.894716, c_c=5.558657, c_d=-0.11829, c_e=-1.9818, c_f=-4.50339, c_g=-11.4625, c_h=7.461454, c_i=5.299396, c_j=4.76657, c_k=-2.3127, c_l=-3.42739)

    Albedo (rel.) calculated according to Duffková and Brom et al. (2012)

    Parameters: | ndvi (numpy.array) – Normalized Difference Vegetation Index (-) msavi – Modified Soil Adjusted Vegetation Index (-) according to Gao et al. 1996. c_a (float) – constant. Default a = 0.08611 c_b (float) – constant. Default a = 0.894716 c_c (float) – constant. Default a = 5.558657 c_d (float) – constant. Default a = -0.11829 c_e (float) – constant. Default a = -1.9818 c_f (float) – constant. Default a = -4.50339 c_g (float) – constant. Default a = -11.4625 c_h (float) – constant. Default a = 7.461454 c_i (float) – constant. Default a = 5.299396 c_j (float) – constant. Default a = 4.76657 c_k (float) – constant. Default a = -2.3127 c_l (float) – constant. Default a = -3.42739
    Returns: | Albedo (rel.)
    Return type: | numpy.ndarray

    References:

    Duffková, R., Brom, J., Žížala, D., Zemek, F., Procházka, J., Nováková, E., Zajíček, A., Kvítek, T., 2012. Určení infiltračních oblastí pomocí vodního stresu vegetace na základě dálkového průzkumu Země a pozemních měření. Certifikovaná metodika. VÚMOP, v.v.i., Praha.

  `albedoLandsat`(blue, green, red, nir, swir1, swir2, sat_type='L8')

    Albedo (rel.) calculated for Landsat satellite sensors. Albedo for Landsat 4 TM, 5 TM and Landsat 7 ETM+ is calculated according to Tasumi et al. (2008). Albedo for Landsat 8 OLI/TIRS is calculated according to Olmeo et al. (2017). Albedo is computed with spectral reflectance bands on relative scale (0 to 1).

    Note: This algorithm might be used with another data from different devices, however a comparable spectral data (bands) should be used.

    Parameters: | blue (numpy.ndarray) – Blue band (rel.) green (numpy.ndarray) – Green band (rel.) red (numpy.ndarray) – Red band (rel.) nir (numpy.ndarray) – NIR band (rel.) swir1 (numpy.ndarray) – SWIR1 band on ca 1.61 (rel.) swir2 (numpy.ndarray) – SWIR2 band on ca 2.2 (rel.) sat_type (str) – Type of Landsat satellite: L5 - Landsat 4 TM, 5 TM or Landsat 7 ETM+ L8 - Landsat 8 OLI/TIRS
    Returns: | Albedo (rel.)
    Return type: | numpy.ndarray

    References:

    G.F. Olmedo, S. Ortega-Farias, D. Fonseca-Luengo, D. de la Fuente-Saiz, F.F. Peñailillo 2018: Water: actual evapotranspiration with energy balance models. R Package Version 0.6 (2017)

    Tasumi, M., Allen, R.G., Trezza, R., 2008. At-Surface Reflectance and Albedo from Satellite for Operational Calculation of Land Surface Energy Balance. Journal of Hydrologic Engineering 13, 51–63. https://doi.org/10.1061/(ASCE)1084-0699(2008)13:2(51).

  `atmEmissivity`(e_Z, ta)

    Atmospheric emissivity calculated according to Idso (see Brutsaert 1982).

    Parameters: | e_Z (numpy.ndarray, float) – Atmospheric water vapour pressure (kPa) ta (numpy.ndarray, float) – Air temperature
    Returns: | Air emissivity (rel.)
    Return type: | numpy.ndarray, float

  `downRL`(ta, emis_a)

    Funtion calculates downward flux of longwave radiation

    Parameters: | ta (numpy.ndarray, float) – Air temperature emis_a (numpy.ndarray, float) – Air emissivity (rel.)
    Return RL_in: | Downward flux of longwave radiation
    Rtype RL_in: | numpy.ndarray, float

  `netRad`(Rs_in_corr, Rs_out, RL_in, RL_out)

    Total net radiation.

    Parameters: | Rs_in_corr (numpy.ndarray) – Incomming global (shortwave) radiation Rs_out (numpy.ndarray) – Outgoing (reflected) shortwave radiation RL_in (numpy.ndarray) – Incomming (downward) longwave radiation RL_out (numpy.ndarray) – Outgoing (upward) longwave radiation
    Returns: | Total net radiation flux
    Return type: | numpy.ndarray

  `outRL`(ts, emiss)

    Upward flux of longwave radiation

    Parameters: | ts (numpy.ndarray) – Surface temperature emiss (numpy.ndarray) – Surface emissivity (rel.)
    Returns: | Upward flux of longwave radiation
    Return type: | numpy.ndarray

  `reflectRs`(Rs_in_corr, albedo)

    Amount of shortwave radiation reflected from surface

    Parameters: | Rs_in_corr (numpy.ndarray) – Incomming global radiation corrected on DEM albedo (numpy.ndarray) – Surface albedo (rel.)
    Returns: | Amount of reflected global radiation
    Return type: | numpy.ndarray

  `slopeAspect`(DMT, x_size, y_size)

    Slope and aspect of terrain (DMT) in degrees.

    Parameters: | DMT (numpy.ndarray) – Digital model of terrain (m a.s.l.) x_size (float) – Size of pixel in x axis (m) y_size (float) – Size of pixel in y axis (m)
    Returns: | Slope of the terrain
    Return type: | numpy.ndarray
    Returns: | Aspect of the terrain
    Return type: | numpy.ndarray

  `solarInTopo`(Rs_in, slope, aspect, latitude, longitude, date_acq, time_acq)

    Calculation of incident shortwave solar radiation flux according to the solar geometry, position (latitude and longitude) and shape of surface (slope and orientation). Flux of the solar energy is calculated on basis of the measured global radiation using pyranometer (incomming global radiation). Diffuse part of radiation is not separated in calculation.

    Parameters: | Rs_in (float) – Global radiation measured by pyranometer . slope (numpy.ndarray) – Slope of the terrain . aspect (numpy.ndarray) – Orientation of the terrain . latitude (float) – Mean latitude of the data in decimal degrees longitude (float) – Mean longitude of the data in decimal degrees date_acq (datetime.date) – Date of data acquisition in iso format (‘YYYY-mm-dd’) time_acq (datetime.time) – Time in GMT in datetime.time format (‘HH:MM:SS.SS’)
    Returns: | Incident shortwave radiation corrected on the terrain and solar geometry.
    Return type: | numpy.ndarray

class `SEBCS_lib.``VegIndices`

  Calculation of vegetation indices from spectral data.

  `LAI`(red, nir, method=2)

    Leaf Area Index (LAI) calculated according to several methods.

    Parameters: | red (numpy.ndarray) – Spectral reflectance in RED region (rel.) nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.) method (int) – Method of LAI calculation: 0: Pôças 1: Bastiaanssen 2: Jafaar (default) 3: Anderson 4: vineyard 5: Carrasco 6: Turner 7: Haboudane 8: Brom (experimental)
    Returns: | Leaf Area Index (LAI)
    Return type: | numpy.ndarray

    References

    Anderson, M., Neale, C., Li, F., Norman, J., Kustas, W., Jayanthi, H., Chavez, J., 2004. Upscaling ground observations of vegetation water content, canopy height, and leaf area index during SMEX02 using aircraft and Landsat imagery. Remote Sensing of Environment 92, 447–464. https://doi.org/10.1016/j.rse.2004.03.019

    Bastiaanssen, W.G.M., Menenti, M., Feddes, R.A., Holtslag, A.A.M., 1998. A remote sensing surface energy balance algorithm for land ( SEBAL). 1. Formulation. Journal of Hydrology 212–213, 198–212. https://doi.org/10.1016/S0022-1694(98)00253-4

    Carrasco-Benavides, M., Ortega-Farías, S., Lagos, L., Kleissl, J., Morales-Salinas, L., Kilic, A., 2014. Parameterization of the Satellite-Based Model (METRIC) for the Estimation of Instantaneous Surface Energy Balance Components over a Drip-Irrigated Vineyard. Remote Sensing 6, 11342–11371. https://doi.org/10.3390/rs61111342

    Jaafar, H.H., Ahmad, F.A., 2019. Time series trends of Landsat-based ET using automated calibration in METRIC and SEBAL: The Bekaa Valley, Lebanon. Remote Sensing of Environment S0034425718305947. https://doi.org/10.1016/j.rse.2018.12.033

    Pôças, I., Paço, T.A., Cunha, M., Andrade, J.A., Silvestre, J., Sousa, A., Santos, F.L., Pereira, L.S., Allen, R.G., 2014. Satellite-based evapotranspiration of a super-intensive olive orchard: Application of METRIC algorithms. Biosystems Engineering 128, 69–81. https://doi.org/10.1016/j.biosystemseng.2014.06.019

    Turner, D.P., Cohen, W.B., Kennedy, R.E., Fassnacht, K.S., Briggs, J.M., 1999. Relationships between Leaf Area Index and Landsat TM Spectral Vegetation Indices across Three Temperate Zone Sites. Remote Sensing of Environment 70, 52–68. https://doi.org/10.1016/S0034-4257(99)00057-7

  `biomass_sat`(ndvi)

    Calculation of amount of fresh biomass from satellite data. NDVI is used for estimation

    Parameters: | ndvi – Normalized Difference Vegetation Index (NDVI).
    Returns: | Amount of fresh biomass

  `fractVegCover`(ndvi)

    Fractional vegetation cover layer - Fc.

    Parameters: | ndvi (numpy.ndarray) – Normalized Difference Vegetation Index - NDVI (unitless)
    Returns: | Fractional vegetation cover layer - Fc (unitless)
    Return type: | numpy.ndarray

  `vegHeight`(h_min, h_max, msavi)

    Height of effective vegetation cover (m) derived from MSAVI index according to Gao et al. (2011).

    Parameters: | h_min (numpy.ndarray) – Maximal height of vegetation cover (m) h_max (numpy.ndarray) – Minimal height of vegetation cover (m) msavi (numpy.ndarray) – Modified Soil Adjusted Vegetation Index (MSAVI)
    Returns: | Effective vegetation cover height (m)
    Return type: | numpy.ndarray

    References

    Gao, Z.Q., Liu, C.S., Gao, W., Chang, N.-B., 2011. A coupled remote sensing and the Surface Energy Balance with Topography Algorithm (SEBTA) to estimate actual evapotranspiration over heterogeneous terrain. Hydrol. Earth Syst. Sci. 15, 119–139. https://doi.org/10.5194/hess-15-119-2011

  `viMSAVI`(red, nir)

    Modified Soil Adjusted Vegetation Index - MSAVI (Qi et al. 1994).

    Parameters: | red (numpy.ndarray) – Spectral reflectance in RED region (rel.) nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)
    Returns: | Modified Soil Adjusted Vegetation Index - SAVI (unitless)
    Return type: | numpy.ndarray

    References

    Qi, J., Chehbouni, A., Huete, A.R., Kerr, Y.H., Sorooshian, S., 1994. A modified soil adjusted vegetation index. Remote Sensing of Environment 48, 119–126. https://doi.org/10.1016/0034-4257(94)90134-1

  `viNDMI`(nir, swir1)

    Normalized Vegetation Moisture Index - NDMI.

    Parameters: | nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.) swir1 – Spectral reflectance in SWIR region (approx. 1.61 (rel.)
    Returns: | Normalized Vegetation Moisture Index - NDMI (unitless)
    Return type: | numpy.ndarray

  `viNDVI`(red, nir)

    Normalized Difference Vegetation Index - NDVI.

    Parameters: | red (numpy.ndarray) – Spectral reflectance in RED region (rel.) nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)
    Returns: | Normalized Difference Vegetation Index - NDVI (unitless)
    Return type: | numpy.ndarray

  `viOSAVI`(red, nir, L=0.16)

    Optimized Soil Adjusted Vegetation Index - OSAVI (Rondeaux et al. ( 1996)).

    Parameters: | red (numpy.ndarray) – Spectral reflectance in RED region (rel.) nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.) L (float) – Parameter L. Default L=0.5
    Returns: | Soil Adjusted Vegetation Index - OSAVI (unitless)
    Return type: | numpy.ndarray

    References

    Rondeaux G., Steven M., Baret F. (1996): Optimisation of soil-adjusted vegetation indices Remote Sensing of Environment, 55 (1996), pp. 95-107

  `viRDVI`(red, nir)

    Renormalized Difference Vegetation Index - RDVI (Roujean and Breon, 1995).

    Parameters: | red (numpy.ndarray) – Spectral reflectance in RED region (rel.) nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.)
    Returns: | RDVI
    Return type: | numpy.ndarray

    References

    Roujean, J.-L., Breon, F.-M., 1995. Estimating PAR absorbed by vegetation from bidirectional reflectance measurements. Remote Sensing of Environment 51, 375–384. https://doi.org/10.1016/0034-4257(94)00114-3

  `viSAVI`(red, nir, L=0.5)

    Soil Adjusted Vegetation Index - SAVI (Huete, 1988).

    Parameters: | red (numpy.ndarray) – Spectral reflectance in RED region (rel.) nir (numpy.ndarray) – Spectral reflectance in NIR region (rel.) L (float) – Parameter L. Default L=0.5
    Returns: | Soil Adjusted Vegetation Index - SAVI (unitless)
    Return type: | numpy.ndarray

    References

    Huete A.R. (1988): A soil-adjusted vegetation index (SAVI) Remote Sensing of Environment 27, 47-57.

class `SEBCS_lib.``WindStability`

  Atmospheric stability calculation. Class includes methods for calculation of boundary layer stability, friction velocity and aerodynamic resistance of the surface. Methods for calculation of stability parameters for both aerodynamic and gradient methods are included. Methods for SEBAL procedure are also used. Some another features are included.

  `aeroSEBAL`(Uz, ta, ts, z0m, Rn, G, rho, niter=10, Z=200, z1=0.1, z2=2, cp=1012.0, kappa=0.41, mask=None)

    Calculation of sensible heat flux and surface aerodynamic resistance according to Bastiaanssen et al. (1998).

    Parameters: | Uz (numpy.ndarray) – Wind speed at level Z ta (numpy.ndarray) – Air temperature at blending height ts (numpy.ndarray) – Surface temperature z0m (numpy.ndarray) – Surface roughness for momentum transfer (m) Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux rho (numpy.ndarray) – Specific air density niter (int) – Number of iteration Z (float (Numpy array)) – Blending height (mixing layer height) (m). Default 200 m. z1 (float) – First height above zero plane displacement (m) z2 (float) – Second height above zero plane displacement (m) cp (float) – Thermal heat capacity of dry air kappa (float) – von Karman constant. Default 0.41 mask – Mask of the area of interest. Number of rows and columns

    should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray

    Returns: | Aerodynamic resistance for heat transfer calculated according to SEBAL (Bastiaanssen et al. 1998)
    Return type: | numpy.ndarray
    Returns: | Sensible heat flux calculated according to SEBAL (Bastiaanssen et al. 1998)
    Return type: | numpy.ndarray

  static `coefX`(Z, L)

    X coefficient for atmospheric stability calculation.

    Parameters: | Z (float) – Blending height (mixing layer height) (m). Default 200 m. L (numpy.ndarray) – Monin-Obukhov length (m)
    Returns: | X coefficient for atmospheric stability calculation
    Return type: | numpy.ndarray

  static `coef_a`(t_wet, cb)

    Coefficient a calculated from temperature gradient.

    Parameters: | t_wet (numpy.ndarray) – Temperature for wet surface cb (numpy.ndarray) – Coefficient b calculated from temperature gradient
    Returns: | Coefficient a calculated from temperature gradient
    Return type: | numpy.ndarray

  static `coef_b`(t_dry, t_wet, t_max, ta)

    Coefficient b calculated from temperature gradient.

    Parameters: | t_dry (float, numpy.ndarray) – Temperature for dry surface derived from the surface temperature layer t_wet (float, numpy.ndarray) – Temperature for wet surface derived from the surface temperature layer t_max (numpy.ndarray) – Maximal surface temperature calculated from energy balance ta (numpy.ndarray) – Air temperature at level Z
    Returns: | Coefficient a calculated from temperature gradient
    Return type: | numpy.ndarray

  `dT`(ts, ta, Rn, G, ra, rho, cp=1012.0, mask=None)

    Temperature gradient calculated according to SEBAL (Bastiaanssen et al. 1998).

    Parameters: | ts (numpy.ndarray) – Surface temperature ta (numpy.ndarray) – Air temperature at level Z Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux ra (numpy.ndarray) – Aerodynamic resistance rho (numpy.ndarray) – Specific air density cp (float) – Thermal heat capacity of dry air mask – Mask of the area of interest. Number of rows and columns

    should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray :return: Temperature difference dT calculated according to Bastiaanssen (1998) :rtype: numpy.ndarray

  static `dryT`(ts, mask=None)

    Extraction of temperature for dry surface with no evaporation.

    Parameters: | ts (numpy.ndarray) – Surface temperature mask – Mask of the area of interest. Number of rows and columns

    should be the same. Format (1, 0) or (1, nan). :type mask: numpy.ndarray

    Returns: | Temperature of dry surface derived from surface temperature layer.
    Return type: | float

  static `frictVelo`(Uz, z0m, disp=0.0, Z=200.0, psi_m=0, kappa=0.41)

    Friction velocity of wind speed corrected on atmospheric stability.

    Parameters: | disp (numpy.ndarray, float) – Uz (numpy.ndarray) – Wind speed at Z level z0m (numpy.ndarray, float) – Surface roughness for momentum transfer (m) disp – Zero plane displacement (m) Z (float) – Blending height (mixing layer height) (m). Default 200 m. psi_m (numpy.ndarray) – Stability parameter for momentum transfer. Defaul 0. kappa (float) – von Karman constant. Default 0.41
    Returns: | Friction velocity
    Return type: | numpy.ndarray

  static `lengthMO`(frict, ts, flux_H=None, rho=None, t_virt=None, cp=1012, kappa=0.41, gravit=9.81)

    Monin-Obukhov length (m)

    Parameters: | frict (numpy.ndarray) – Friction velocity ts (numpy.ndarray) – Surface temperature (C degree) flux_H (numpy.ndarray) – Sensible heat flux (W.m2) rho (numpy.ndarray) – Specific air density t_virt (numpy.ndarray) – Virtual temperature cp (float) – Thermal heat capacity of dry air kappa (float) – von Karman constant. Default 0.41 gravit (float) – Gravitation forcing (m/s2). Default 9.81
    Returns: | Monin-Obukhov length (m)
    Return type: | numpy.ndarray

  static `maxT`(Rn, G, ra, ta, rho, cp=1012.0)

    Maximal surface temperature calculated on physical basis (K).

    Parameters: | Rn (numpy.ndarray) – Total net radiation G (numpy.ndarray) – Ground heat flux ra (numpy.ndarray) – Aerodynamic resistance for heat transfer ta (numpy.ndarray) – Air temperature at level Z rho (numpy.ndarray) – Specific air density cp (float) – Thermal heat capacity of dry air
    Returns: | Maximal surface temperature calculated from energy balance equation
    Return type: | numpy.ndarray

  static `psiH`(L, X, Z=200, a=1.0, b=0.667, c=5.0, d=0.35)

    Calculation of stability parameter for heat transfer (-) according to Beljaars et Holstag (1991) for stable conditions and Liu et al. (2007) for unstable and neutral conditions.

    Parameters: | L (numpy.ndarray) – Monin-Obukhov length (m) X (numpy.ndarray) – X coefficient for stability calculation Z (float) – Blending height (mixing layer height) (m). Default 200 m. a (float) – Coefficient. Default a = 1.0 b (float) – Coefficient. Default b = 0.667 c (float) – Coefficient. Defalt c = 5.0 d (float) – Coefficient. Default d = 0.35
    Returns: | Stability parameter for momentum transfer (-)
    Return type: | numpy.ndarray

  static `psiM`(L, X, Z=200, a=1.0, b=0.667, c=5.0, d=0.35)

    Calculation of stability parameter for momentum transfer (-) according to Beljaars et Holstag (1991) for stable conditions and Liu et al. (2007) for unstable and neutral conditions.

    Parameters: | L (numpy.ndarray) – Monin-Obukhov length (m) X (numpy.ndarray) – X coefficient for stability calculation Z (float) – Blending height (mixing layer height) (m). Default 200 m. a (float) – Coefficient. Default a = 1.0 b (float) – Coefficient. Default b = 0.667 c (float) – Coefficient. Defalt c = 5.0 d (float) – Coefficient. Default d = 0.35
    Returns: | Stability parameter for momentum transfer (-)
    Return type: | numpy.ndarray

  static `raGrad`(flux_H, rho, ts, ta, cp=1012)

    Aerodynamic resistance for heat and momentum transfer (s.m^{-1}) calculated from conversion of sensible heat flux equation.

    Parameters: | flux_H (numpy.ndarray) – Sensible heat flux rho (numpy.ndarray) – Specific air density ts – Surface temperature ta (numpy.ndarray) – Air temperature at level Z cp (float) – Thermal heat capacity of dry air
    Returns: | Aerodynamic resistance for gradient model
    Return type: | numpy.ndarray

  static `raSEBAL`(frict, psiH_z1, psiH_z2, z1=0.1, z2=2.0, kappa=0.41)

    Calculation of surface aerodynamic resistance for heat transfer based on SEBAL approach (Bastiaanssen, 1998).

    Parameters: | frict (numpy.ndarray) – Friction velocity psiH_z1 (numpy.ndarray) – Stability parameter for momentum transfer (-) at level z1 psiH_z2 (numpy.ndarray) – Stability parameter for momentum transfer (-) at level z2 z1 (float) – First height above zero plane displacement (m) z2 (float) – Second height above zero plane displacement (m) kappa (float) – von Karman constant. Default 0.41
    Returns: | Aerodynamic resistance for heat transfer based on SEBAL approach (Bastiaanssen, 1998).
    Return type: | numpy.ndarray

  static `raThom`(Uz, z0m, z0h, disp=0.0, psi_m=0.0, psi_h=0.0, Z=200.0, kappa=0.41)

    Aerodynamic resistance for heat and momentum transfer (s.m-1) calculated according to Thom (1975).

    Parameters: | disp (numpy.ndarray, float) – Uz (numpy.ndarray) – Wind speed at level Z z0m (numpy.ndarray) – Surface roughness for momentum transfer (m) z0h (numpy.ndarray) – Surface roughness for heat transfer (m) disp – Zero plane displacement (m) psi_m (numpy.ndarray) – Stability parameter for momentum transfer (-). Default is 0. psi_h (numpy.ndarray) – Stability parameter for heat transfer (-) Default is 0. Z (float (Numpy array)) – Blending height (mixing layer height) (m). Default 200 m. kappa (float) – von Karman constant. Default 0.41
    Return ra: | Aerodynamic resistance for heat and momentum transfer (s.m-1) calculated according to Thom (1975)
    Rtype ra: | numpy.ndarray

    References

    Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.

  `stabCoef`(Uz, ta, ts, z0m, z0h, disp=0, Z=200, L=-10000.0, n_iter=10, a=1.0, b=0.667, c=5.0, d=0.35, kappa=0.41, gravit=9.81)

    Stability parameters calculation using iterative procedure described by Itier (1980).

    Parameters: | disp (numpy.ndarray, float) – Uz (numpy.ndarray) – Wind speed at level Z ta (numpy.ndarray) – Air temperature at Z level (K, C degrees) ts (numpy.ndarray) – Surface temperature (K, C degrees) z0m (numpy.ndarray) – Surface roughness for momentum transfer (m) z0h (numpy.ndarray) – Surface roughness for heat transfer (m) disp – Zero plane displacement (m) Z (float (Numpy array)) – Blending height (mixing layer height) (m). Default 200 m. L (float) – Initial value of Monin-Obukhov length (m). Default -10000.0 n_iter (int) – Number of iteration a (float) – Coefficient. Default a = 1.0 b (float) – Coefficient. Default b = 0.667 c (float) – Coefficient. Defalt c = 5.0 d (float) – Coefficient. Default d = 0.35 kappa (float) – von Karman constant. Default 0.41 gravit (float) – Gravitation forcing (m/s2). Default 9.81
    Returns: | Stability parameter for momentum transfer (-)
    Return type: | numpy.ndarray
    Returns: | Stability parameter for heat transfer (-)
    Return type: | numpy.ndarray
    Returns: | Friction velocity .
    Return type: | numpy.ndarray
    Returns: | Monin-Obukhov length (m)
    Return type: | numpy.ndarray

  static `virtTemp`(ta, ts, z0h, disp=0.0, Z=200, psi_h=0, kappa=0.41)

    Virtual temperature (K) corrected on atmospheric stability.

    Parameters: | disp (numpy.ndarray, float) – ta (numpy.ndarray) – Air temperature at Z level (K, C degrees) ts (numpy.ndarray) – Surface temperature (K, C degrees) z0h (numpy.ndarray) – Surface roughness for heat transfer (m) disp – Zero plane displacement (m) Z (float) – Blending height (mixing layer height) (m). Default 200 m. psi_h (numpy.ndarray) – Stability parameter for heat transfer, Default 0. kappa (float) – von Karman constant. Default 0.41
    Returns: | Virtual temperature (K)
    Return type: | numpy.ndarray

  static `wetT`(ta)

    Surface temperature for wet surface. In this case surface temperature for wet surface is equal to air temperature. This statement follows from imagine that the LE = Rn - G and thus H is close to zero.

    Parameters: | ta (numpy.ndarray) – Air temperature at level Z
    Returns: | Temperature of wet surface.
    Return type: | numpy.ndarray

  static `windSpeedZ`(U, Z=200.0, Z_st=2.0, h_st=0.12, ws_homog=1)

    Wind speed recalculated to height Z according to logarithmic law (Gao et al. 2011). The results can contain simple number, homogenous or heterogenous matrix of data (Numpy array).

    Parameters: | U (float, numpy.ndarray) – Wind speed measured on meteostation at level Z_st . Z (float) – Blending height (mixing layer height) (m). Default 200 m. Z_st (float) – Height of wind speed measurement (m). Default 2 m. h_st (float) – Height of vegetation cover under meteostation (m). Default value is 0.12 m which corresponds with reference cover used for meteostations. ws_homog – Indicates if the result matrix contains uniform

    result (mean value of wind speed for the area) or if the results includes heterogeneity of input data (each pixel is calculated separately). 0 - homogenous, 1 - heterogenous :type ws_homog: int :return: Wind speed at mixing layer :rtype: float, numpy.ndarray

    References

    Gao, Z.Q., Liu, C.S., Gao, W., Chang, N.B., 2011. A coupled remote sensing and the Surface Energy Balance with Topography Algorithm (SEBTA) to estimate actual evapotranspiration over heterogeneous terrain. Hydrol. Earth Syst. Sci. 15, 119–139. https://doi.org/10.5194/hess-15-119-2011

  static `z0h`(z0m)

    Aerodynamic roughness of the surface for heat transfer (m) calculated according to Thom (1975).

    Parameters: | z0m (numpy.ndarray, float) – Aerodynamic roughness of the surface for momentum transfer (m)
    Returns: | Aerodynamic roughness of the surface for heat transfer (m)
    Return type: | numpy.ndarray, float

    References

    Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.

  static `z0m`(h_eff, LAI)

    Aerodynamic roughness of the surface for momentum transfer (m). z0m is calculated according to Tasumi (2003) for vegetation cover lower tha 1 m and according to Thom (1975) for vegetation cover higher than 1 m. The lowest value of z0m is 0.005, which is typical value for agricultural bare soils (Allen et al. 2007)

    Parameters: | h_eff (numpy.ndarray) – Effective vegetation cover height (m) LAI (numpy.ndarray) – Leaf Area Index
    Returns: | Aerodynamic roughness of the surface for momentum transfer (m)
    Return type: | numpy.ndarray

    References

    Allen, R.G., Tasumi, M., Trezza, R., 2007. Satellite-Based Energy Balance for Mapping Evapotranspiration with Internalized Calibration (METRIC)—Model. J. Irrig. Drain Eng. 133, 380–394. https://doi.org/10.1061/(ASCE)0733-9437(2007)133:4(380)

    Tasumi, M., 2003. Progress in Operational Estimation of Regional Evapotranspiration Using Satellite Imagery (Ph.D. Thesis). University of Idaho, Moscow, Idaho.

    Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.

  static `zeroPlaneDis`(h_eff)

    Zero plane displacement (m) calculated according to Thom (1975).

    Parameters: | h_eff (numpy.ndarray) – Effective vegetation cover height (m)
    Returns: | Zero plane displacement (m)
    Return type: | numpy.ndarray

    References

    Thom, A.S., 1975. Momentum, mass and heat exchange of plant communities, in: Monteith, J.L. (Ed.), Vegetation and the Atmosphere, Vol. 1 Principles. Academic Press, London, pp. 57–110.